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## Idea

A Horn theory is a theory in which every axiom has a certain special form.

## Definition

Let $\Sigma$ be a signature. A term of $\Sigma$ is an expression built out of variables and function symbols. (For example, $x y^{-1} z$ is a term in the language of groups.) An atomic formula relative to $\Sigma$ is a formula that consists of a relation symbol of $\Sigma$ (including equality) applied to terms.

A Horn clause is a logical expression of the form

$\phi_1 \wedge \ldots \wedge \phi_n \vdash \phi$

where each $\phi_i$ and $\phi$ is atomic. A (universal) Horn theory is a theory in which every axiom is a Horn clause.

Last revised on August 25, 2012 at 21:44:45. See the history of this page for a list of all contributions to it.